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Probing properties of nuclear spin-orbit interaction with nucleon spin polarization in intermediate-energy heavy-ion collisions

T0 review · 2 major / 4 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read The paper claims that the perpendicular spin polarization $P_y$ of free nucleons in 100A MeV Au+Au collisions encodes the strength, density dependence, and isospin dependence of the nuclear spin-orbit interaction, with each property…

desk verdict A clean forward-model sensitivity scan identifying Py signatures for spin-orbit strength, density, and isospin dependence, but the 'good probe' claim rests on an unquantified spin-survival assumption in the collision term. read the letter →

arxiv 2502.04687 v1 pith:236N5SC6 submitted 2025-02-07 nucl-th hep-exnucl-ex

Jun Xu This is my paper · ORCID
classification nucl-thhep-exnucl-ex
keywords nuclearspin-orbitinteractionspinpolarizationheavy-ioncollisionsBoltzmann-Uehling-Uhlenbecktransportdensitydependenceisospinintermediatebeamenergyfreenucleonobservables
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that a single measurable quantity, the spin polarization $P_y$ of free nucleons perpendicular to the reaction plane, can reveal three poorly known properties of the nuclear spin-orbit interaction: its overall strength, its density dependence, and its isospin dependence. In Au+Au collisions at 100A MeV simulated with a spin- and isospin-dependent Boltzmann-Uehling-Uhlenbeck (SIBUU) transport model, each property leaves a distinct signature in $P_y$ as a function of rapidity and transverse momentum. A weaker coupling lowers $P_y$; making the coupling density-dependent through $W_0^* = W_0(\rho/\rho_0)^\gamma$ raises $P_y$ at large rapidities and at high transverse momenta; and the difference in $P_y$ between free neutrons and protons at midrapidity and low transverse momentum follows the isospin dependence. If true, heavy-ion collision data can complement nuclear-structure fits in pinning down the spin-orbit interaction, and the same observable links to the measured spin polarization of $\Lambda$ hyperons at higher energies.

What carries the argument

The carrying mechanism is the spin-and-isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model, in which nucleon spin is an extra degree of freedom precessing under the nuclear spin-orbit potential. In the lattice-Hamiltonian implementation, the spin-orbit part of the single-particle energy is $V_{so} = -\frac{W_0^*}{2}[\alpha(\rho\nabla\cdot\mathbf{J} + \mathbf{s}\cdot\nabla\times\mathbf{j}) + \beta\sum_\tau(\rho_\tau\nabla\cdot\mathbf{J}_\tau + \mathbf{s}_\tau\cdot\nabla\times\mathbf{j}_\tau)]$, and the spin expectation vector precesses as $d\boldsymbol{\sigma}_i/dt = 2\mathbf{h}\times\boldsymbol{\sigma}_i$, with $\mathbf{h}$ built from density gradients and currents. That precession converts the orbital angular momentum of the non-central collision into net spin polarization. The paper varies the coupling coefficient $W_0^* = W_0(\rho/\rho_0)^\gamma$ to mimic density dependence and the coefficients $\alpha,\beta$ to mimic isospin dependence, then reads the resulting rapidity and transverse-momentum dependence of $P_y$. The spin precession driven by the spin-orbit mean field, scored through the polarization of final free nucleons, is the machinery that carries the argument.

What would settle it

Run the same SIBUU simulation with a collision term that stochastically rotates or flips nucleon spins after every scattering, using realistic spin-dependent amplitudes, and check whether the distinctive rapidity and $p_T$ signatures of $P_y$ survive; if they are erased, the proposed probe is not robust. A direct measurement of $P_y$ of free nucleons in 100A MeV Au+Au collisions showing no enhancement at large rapidities and no neutron-proton splitting at low $p_T$ would also falsify the specific predictions.

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Extended reading notes

Core claim

The central claim is that the perpendicular spin polarization $P_y$, defined as $(N_{s_y=+1/2} - N_{s_y=-1/2})/(N_{s_y=+1/2} + N_{s_y=-1/2})$ for final free nucleons, is a good probe of the strength, density dependence, and isospin dependence of the nuclear spin-orbit interaction. Simulating mid-central ($b=8$ fm) and mid-peripheral ($b=12$ fm) Au+Au collisions at 100A MeV, the paper finds that $P_y$ is larger for $W_0^* = 150$ MeV fm$^5$ than for 80 MeV fm$^5$, and stronger in mid-peripheral than in mid-central collisions. A density-dependent coefficient $W_0^* = W_0(\rho/\rho_0)$ keeps $P_y$ similar at midrapidity but makes it larger at large rapidities and less negative or larger at high $p_T$, because the interaction is enhanced in the high-density participant matter. Changing the isospin structure from ($\alpha=1,\beta=1$) to ($\alpha=2,\beta=-1$) reverses the neutron-proton ordering of $P_y$ at midrapidity and small $p_T$. The longitudinal polarization $P_z$ also responds to the coupling strength and density dependence, but its azimuthal pattern is not a clean isospin probe, so the paper's conclusion is that $P_y$ is the informative observable.

Load-bearing premise

The load-bearing assumption is that a nucleon's spin direction is unchanged after each successful binary collision, based on an estimate from a realistic nucleon-nucleon potential; if real collisions depolarize or flip spins, the predicted $P_y$ rapidity and $p_T$ patterns would be weakened or reshaped and the probe would lose its clear signatures.

Editorial extensions

If this is right

  • A measurement of $P_y$ for free nucleons in 100A MeV Au+Au collisions would directly test the strength of the nuclear spin-orbit coupling, since the polarization scales with $W_0^*$ between 80 and 150 MeV fm$^5$.
  • The rapidity dependence of $P_y$ is a test of density dependence: a density-dependent coupling leaves $P_y$ at midrapidity nearly unchanged but produces an excess at large rapidities.
  • The neutron-proton difference in $P_y$ at midrapidity and low $p_T$ discriminates between isospin parametrizations of the spin-orbit functional.
  • Mid-peripheral collisions ($b=12$ fm) give a cleaner, stronger polarization signal than mid-central ones, so future measurements should favor peripheral selection.
  • The longitudinal polarization $P_z$ is a weaker diagnostic: it senses the coupling strength and density dependence but cannot cleanly resolve isospin dependence, steering experimental attention to $P_y$.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Implicit in the paper is that a dedicated intermediate-energy experiment with spin-sensitive detection of free neutrons and protons could extract spin-orbit parameters dynamically, providing a collision-based complement to nuclear-structure constraints; the author does not propose such an experiment.
  • The clean $P_y$ signatures depend on nucleon spins surviving binary collisions unchanged; including realistic spin-changing collisions would likely smear the patterns, so the practical discriminating power of the probe may be weaker than the idealized calculation suggests.
  • The same framework could be run with a series of $\alpha,\beta$ values and systems of varying $N/Z$ to map the isospin dependence as a continuous function rather than comparing two discrete parametrizations.
  • Because the calculation sits at 100A MeV, it offers a bridge from nucleonic transport to the $\Lambda$ spin-polarization signals measured at higher beam energies, though the paper itself does not draw that connection.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. This paper presents a transport-model study of nucleon spin polarization in Au+Au collisions at 100A MeV, using a spin- and isospin-dependent Boltzmann-Uehling-Uhlenbeck (SIBUU) model with a mean-field spin-orbit interaction. The author computes the polarization perpendicular to the reaction plane (Py) and along the beam direction (Pz) for free nucleons and examines their sensitivity to the strength (W0), density dependence (parameter gamma in W0* = W0(rho/rho0)^gamma), and isospin dependence (parameters alpha, beta) of the nuclear spin-orbit interaction. The central claim is that Py is a good probe of all three properties, with specific signatures: density dependence enhances Py at large rapidities and high transverse momenta, and isospin dependence shows up in the neutron-proton difference of Py at midrapidity and low transverse momenta. The paper also reports an azimuthal-angular dependence of Pz with a sign that depends on transverse momentum and centrality.

Significance. If the results hold, the paper provides concrete, falsifiable predictions: the spin polarization of free nucleons in intermediate-energy heavy-ion collisions can be used to extract properties of the nuclear spin-orbit interaction that are difficult to determine from nuclear structure alone. The specific signatures—enhanced Py at large rapidities and high pT for density-dependent coupling, and the neutron-proton splitting at midrapidity for isospin-dependent coupling—are experimentally testable in principle. The model is built on standard equations of motion for spin precession and a lattice Hamiltonian method, and the parameter choices are clearly stated. The main concern is that the collision term treats nucleon spins as unchanged after scattering, an assumption that is cited but not quantitatively validated; this is the load-bearing step for the probe claim.

major comments (2)
  1. [Collision-term paragraph (after Eq. (17))] The treatment of spin in the collision term is under-specified. The paper assumes spins are unchanged after successful collisions (citing Refs. [32,33]) without reproducing a quantitative estimate or giving a bound on spin-flip probability or spin relaxation time relative to the collision interval. At the same time, the collision term uses spin-singlet and spin-triplet cross sections, so spin-dependent scattering can itself generate or remove polarization. Since AV18 includes tensor and spin-orbit forces, depolarization may be non-negligible at c.m. energies up to about 50 MeV in 100A MeV Au+Au collisions. The manuscript does not separate the collision-driven contribution from the mean-field spin-orbit torque, nor does it test sensitivity to the assumption. I recommend adding (i) the quantitative estimate from Refs. [32,33], (ii) a sensitivity run with randomly rotated spins after collisions, and (iii) a W0=0 baseline to quantify the collision-only polarization. Without these, the connection between Py and the nuclear spin-orbit properties is not fully secured.
  2. [Eq. (4) and Figs. 2-3] The claim that Py is a good probe of the density dependence of the spin-orbit interaction rests on a comparison between only gamma=0 and gamma=1 in Eq. (4). A two-point comparison cannot establish a robust signature; the effect might be specific to the chosen power-law form W0*(rho/rho0)^gamma. I suggest scanning at least one intermediate value (e.g., gamma=0.5) or providing a theoretical motivation for the functional form, to demonstrate that the observed enhancement at large rapidities and high pT is a monotonic and distinctive feature rather than an artifact of the two chosen values.
minor comments (4)
  1. [Collision-term paragraph] The sentence 'The spins of nucleons after a successful collisions are assumed to be unchanged' contains a grammatical error; 'a successful collisions' should be 'a successful collision'.
  2. [Eq. (5)] The notation 'VM ID' in Eq. (5) is unclear; it should be typeset as V_MID or defined explicitly in the text to avoid confusion with other quantities.
  3. [Eq. (17)] The symbol tau in Eq. (17) is used without an explicit statement that it denotes the isospin of the nucleon i whose equation of motion is being written, in contrast to the summed isospin index tau in Eq. (3). Please clarify this notation.
  4. [Fig. 2 caption] The notation 'yr/ybeam r' in the Fig. 2 caption is ambiguous; please use consistent sub/superscript notation such as y_r/y_beam^r.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper is a forward transport sensitivity study whose Py response to spin-orbit parameters is computed from stated equations, not fitted to or defined from the target observable.

full rationale

The paper's central claim is that Py of free nucleons can serve as a probe of the strength, density dependence, and isospin dependence of the nuclear spin-orbit interaction. The calculation is a forward model: spin-orbit parameters (W0, gamma, alpha, beta) are inputs, and the spin polarization is evolved using the explicitly stated equations of motion, Eq. (16) with the mean-field torque h in Eq. (17), plus the spin-dependent BUU transport framework of Eq. (1). Varying W0, setting W0* = W0(rho/rho0)^gamma, and changing alpha,beta are sensitivity tests, not fits to Py; no experimental Py datum is used to tune these parameters, and no 'prediction' is obtained by inverting the same observable that was fitted. The density-dependent ansatz is introduced openly as a way to mimic different density dependencies, and the resulting rapidity and pT patterns are explained through the density-gradient mechanism in the model, so the output is not equivalent to the input by construction in any formal sense. The one load-bearing approximation is that nucleon spins are unchanged after NN collisions, justified by an estimate from Refs. [32,33] (one self-citation and the AV18 potential). This is a robustness concern rather than a circularity: the estimate is external to the present mapping between spin-orbit parameters and Py, and the paper does not use Py to derive the spin-conservation assumption. The numerous self-citations to earlier SIBUU papers document the model's development, but the essential equations are reproduced in this manuscript, so the derivation chain is self-contained. Overall, there is no circular step that reduces a claimed prediction to its own input.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the assumed spin-orbit interaction form in Eqs. (2)-(4), the semiclassical spin transport in Eq. (16), and the approximation that collisions do not flip spins. The parameters W0, gamma, alpha, beta are chosen by hand from the literature or ad hoc; no free parameters are fit to the target observable Py.

free parameters (4)
  • W0 spin-orbit strength = 150 MeV fm^5 (varied: 80 MeV fm^5 and 150(rho/rho0) MeV fm^5)
    Default from SHF fits in Refs. [11-13]; the central parameter whose probe is claimed.
  • gamma density-dependence exponent = 0 and 1
    Ad hoc in Eq. (4) to mimic different density dependencies; no derivation.
  • alpha, beta isospin coefficients = (1,1) and (2,-1)
    Ad hoc parameter sets in Eq. (3) to represent different isospin dependencies.
  • Momentum-independent mean-field parameters a, b, c, E_sym^pot, gamma_sym = a=-209.2 MeV, b=156.4 MeV, c=1.35, E_sym^pot=18 MeV, gamma_sym=2/3
    Fit to empirical nuclear matter properties; background for the spin-independent potential.
assumptions (6)
  • standard math Spin-dependent BUU transport equation (Eq. 1) with semiclassical test-particle treatment
    Underpins all dynamics; adopted from Refs. [24,25].
  • domain assumption Skyrme-type two-body spin-orbit interaction (Eq. 2) with Hartree-Fock energy density functional (Eq. 3)
    Microscopic origin of the spin-orbit potential; form is assumed from Ref. [27].
  • standard math Spin expectation vector precesses as d sigma_i/dt = 2h x sigma_i (Eq. 16)
    Derived from commutation with H, then semiclassical replacement.
  • ad hoc to paper Nucleon spin is unchanged in successful collisions
    Assumed based on a rough Argonne potential estimate; load-bearing for the polarization signal.
  • domain assumption Free nucleons identified by local density below rho0/8
    Definition of final-state free nucleons used in all observables.
  • domain assumption Spin-dependent NN cross sections from free-space phase-shift analyses
    Collision term input; extracted from Refs. [30,31].

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Cite this review

Pith. "Pith review of Probing properties of nuclear spin-orbit interaction with nucleon spin polarization in intermediate-energy heavy-ion collisions." pith.science (2026). https://pith.science/paper/236N5SC6

@misc{pith2026250204687,
  author       = {Pith},
  title        = {Pith review of: Probing properties of nuclear spin-orbit interaction with nucleon spin polarization in intermediate-energy heavy-ion collisions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/236N5SC6}},
  note         = {Machine review of arXiv:2502.04687}
}
abstract

The nucleon spin polarization perpendicular to the reaction plane ($P_y$) and along the beam direction ($P_z$) in Au+Au collisions at the beam energy of 100A MeV with different nuclear spin-orbit interactions has been studied based on a spin- and isospin-dependent Boltzmann-Uehling-Uhlenbeck (SIBUU) transport model. While the spin polarization is weaker with a weaker nuclear spin-orbit coupling as intuitively expected, a density-dependent nuclear spin-orbit coupling enhances the $P_y$ at large rapidities and leads to a less negative or large $P_y$ at high transverse momenta. The difference in the $P_y$ of free neutrons and protons at midrapidities and at small transverse momenta is sensitive to the isospin dependence of the nuclear spin-orbit interaction. While the $P_z$ is also affected by the properties of nuclear spin-orbit interaction in some sense, the behavior of the $P_y$ serves as a good probe of the strength, density dependence, and isospin dependence of nuclear spin-orbit interaction.

Figures

Figures reproduced from arXiv: 2502.04687 by the authors.

Figure 2
Figure 2. FIG. 2. Rapidity dependence of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 1
Figure 1. FIG. 1. Upper: Contours of the reduced density [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 4
Figure 4. displays the azimuthal angular dependence of the longitudinal spin polarization Pz of free energetic nu￾cleons at midrapidities in mid-central collisions. Here the azimuthal angle is calculated from ϕ = atan2(py, px), with py and px being respectively the nucleon momen￾tum in y and x direction, and Pz is defined similarly to Py as in Eq. (18). It is seen that Pz has negative peaks at ϕ = −3π/4 and π/4 and positive p… view at source ↗
Figures from the paper (1 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Transverse momentum dependence of the second [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Spin polarization from nucleon-nucleon scatterings in intermediate-energy heavy-ion collisions

    nucl-th 2025-06 conditional novelty 5.0 of 10

    Nucleon-nucleon scatterings with phase-shift-derived spin changes and rigorous angular momentum conservation generate 1-2% spin polarization in intermediate-energy heavy-ion collisions.

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Works this paper leans on

38 extracted references · 28 canonical work pages · cited by 1 Pith paper

  1. [1]

    Adamczyk et al

    L. Adamczyk et al. (STAR), Nature 548, 62 (2017)

    work page 2017

  2. [2]

    Adam et al

    J. Adam et al. (STAR Collaboration), Phys. Rev. C 98, 014910 (2018)

    work page 2018

  3. [3]

    Adam et al

    J. Adam et al. (STAR Collaboration), Phys. Rev. Lett. 126, 162301 (2021)

    work page 2021

  4. [4]

    M. S. Abdallah et al. (STAR), Nature 614, 244 (2023)

    work page 2023

  5. [5]

    Adam et al

    J. Adam et al. (STAR Collaboration), Phys. Rev. Lett. 123, 132301 (2019)

    work page 2019

  6. [6]

    M. S. Abdallah et al. (STAR Collaboration), Phys. Rev. C 104, L061901 (2021)

    work page 2021

  7. [7]

    Abou Yassine et al., Physics Letters B 835, 137506 (2022)

    R. Abou Yassine et al., Physics Letters B 835, 137506 (2022)

    work page 2022

  8. [8]

    M. G. Mayer, Phys. Rev. 74, 235 (1948)

    work page 1948

Show all 38 references
  1. [9]

    M. G. Mayer, Phys. Rev. 75, 1969 (1949)

    1949

  2. [10]

    Haxel, J

    O. Haxel, J. H. D. Jensen, and H. E. Suess, Phys. Rev. 75, 1766 (1949)

    1949

  3. [11]

    Lesinski, M

    T. Lesinski, M. Bender, K. Bennaceur, T. Duguet, and J. Meyer, Phys. Rev. C 76, 014312 (2007), arXiv:0704.0731 [nucl-th]

    2007 arXiv

  4. [12]

    Zalewski, J

    M. Zalewski, J. Dobaczewski, W. Satula, and T. R. Werner, Phys. Rev. C 77, 024316 (2008), arXiv:0801.0924 [nucl-th]

    2008 arXiv

  5. [13]

    Bender, K

    M. Bender, K. Bennaceur, T. Duguet, P. H. Heenen, T. Lesinski, and J. Meyer, Phys. Rev. C 80, 064302 (2009), arXiv:0909.3782 [nucl-th]

    2009 arXiv

  6. [14]

    Sorlin and M.-G

    O. Sorlin and M.-G. Porquet, Physica Scripta 2013, 014003 (2012)

    2012

  7. [15]

    Nakada and T

    H. Nakada and T. Inakura, Phys. Rev. C 91, 021302 6 (2015)

    2015

  8. [16]

    M. M. Sharma, G. Lalazissis, J. Konig, and P. Ring, Phys. Rev. Lett. 74, 3744 (1995), arXiv:nucl-th/9502006

    1995 arXiv

  9. [17]

    P. G. Reinhard and H. Flocard, Nucl. Phys. A 584, 467 (1995)

    1995

  10. [18]

    T.-G. Yue, Z. Zhang, and L.-W. Chen, (2024), arXiv:2406.03844 [nucl-th]

    2024

  11. [19]

    T. Zhao, Z. Lin, B. Kumar, A. W. Steiner, and M. Prakash, (2024), arXiv:2406.05267 [nucl-th]

    2024 arXiv

  12. [20]

    J. Xu, B. A. Li, W. Q. Shen, and Y. Xia, Front. Phys. (Beijing) 10, 102501 (2015)

    2015

  13. [21]

    Xu and B

    J. Xu and B. A. Li, Phys. Lett. B 724, 346 (2013)

    2013

  14. [22]

    Y. Xia, J. Xu, B. A. Li, and W. Q. Shen, Phys. Rev. C 89, 064606 (2014)

    2014

  15. [23]

    Xia and J

    Y. Xia and J. Xu, Phys. Lett. B 800, 135130 (2020)

    2020

  16. [24]

    Ring and P

    P. Ring and P. Schuck, The Nuclear Many-Body Problem (Springer, Berlin, 1980)

    1980

  17. [25]

    Smith and H

    H. Smith and H. Jensen, Transport Phenomena(Oxford University Press, Oxford, 1989)

    1989

  18. [26]

    Y. Xia, J. Xu, B. A. Li, and W. Q. Shen, Phys. Lett. B 759, 596 (2016)

    2016

  19. [27]

    Vautherin and D

    D. Vautherin and D. M. Brink, Phys. Rev. C 5, 626 (1972)

    1972

  20. [28]

    Y. M. Engel, D. M. Brink, K. Goeke, S. J. Krieger, and D. Vautherin, Nucl. Phys. A 249, 215 (1975)

    1975

  21. [29]

    R. J. Lenk and V. R. Pandharipande, Phys. Rev. C 39, 2242 (1989)

    1989

  22. [30]

    Y. Xia, J. Xu, B. A. Li, and W. Q. Shen, Phys. Rev. C 96, 044618 (2017)

    2017

  23. [31]

    R. A. Arndt, R. H. Hackman, and L. D. Roper, Phys. Rev. C 15, 1002 (1977)

    1977

  24. [32]

    Liu and J

    R.-J. Liu and J. Xu, Phys. Rev. C 109, 014615 (2024)

    2024

  25. [33]

    R. B. Wiringa, V. G. J. Stoks, and R. Schiavilla, Phys. Rev. C 51, 38 (1995)

    1995

  26. [34]

    Becattini, M

    F. Becattini, M. Buzzegoli, and A. Palermo, Physics Letters B 820, 136519 (2021)

    2021

  27. [35]

    Becattini and I

    F. Becattini and I. Karpenko, Phys. Rev. Lett. 120, 012302 (2018)

    2018

  28. [36]

    B. Fu, S. Y. F. Liu, L. Pang, H. Song, and Y. Yin, Phys. Rev. Lett. 127, 142301 (2021)

    2021

  29. [37]

    S. Y. F. Liu, Y. Sun, and C. M. Ko, Phys. Rev. Lett. 125, 062301 (2020)

    2020

  30. [38]

    Wu, L.-G

    H.-Z. Wu, L.-G. Pang, X.-G. Huang, and Q. Wang, Phys. Rev. Res. 1, 033058 (2019)

    2019

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